Complete and incomplete financial markets in multi-good economies

In several multi-good models in the literature we see in equilibrium that the span of the stocks drop relative to the span of the dividends, which is not a desirable feature. Therefore, in this paper, we investigate conditions for endogenous completeness and incompleteness in continuous-time financial markets driven by diffusion processes with multiple consumption goods and heterogeneous agents. We show that for a class of utility functions, including unit elasticity of substitution, the span of the risky assets is strictly smaller than the span of dividends. We find that, unlike in one-good economies, preferences matter for completeness through relative commodity prices. A sufficient condition for market completeness is that a matrix depending on preferences and dividends is invertible. We show that market completeness can depend on the choice of numeraire good, as changing the numeraire good simultaneously implies a change of the risk-free asset and consequently the asset structure.